Simplify cube root of -243xy^3

$\sqrt[3]{- 243 x y^{3}}$

Step 1

Rewrite $- 243 x y^{3}$ as ${(- 3 y)}^{3} \cdot (9 x)$ .

Factor $- 27$ out of $- 243$ .

$\sqrt[3]{- 27 (9) x y^{3}}$

Rewrite $- 27$ as ${(- 3)}^{3}$ .

$\sqrt[3]{{(- 3)}^{3} \cdot 9 x y^{3}}$

Move $x$ .

$\sqrt[3]{{(- 3)}^{3} \cdot 9 y^{3} x}$

Move $9$ .

$\sqrt[3]{{(- 3)}^{3} y^{3} \cdot 9 x}$

Rewrite ${(- 3)}^{3} y^{3}$ as ${(- 3 y)}^{3}$ .

$\sqrt[3]{{(- 3 y)}^{3} \cdot 9 x}$

Add parentheses.

$\sqrt[3]{{(- 3 y)}^{3} \cdot (9 x)}$

Step 2

Pull terms out from under the radical.

$- 3 y \sqrt[3]{9 x}$